Bringing math into focus

Math is about precision. But for a period in the 1990s, some critics say, math education in the United States veered off that focused track, scattering into an array of topics dubbed “fuzzy,” or a mile wide and an inch deep.

A report issued this month by the National Council of Teachers of Mathematics puts math instruction squarely back on the rails, recommending that teachers in pre-K-8 focus on a few key skills at each grade level.

While the report, “Curriculum Focal Points,” got coverage in the Wall Street Journal and New York Times, local educators say it remains largely harnessed to guidelines the National Council of Teachers of Mathematics spelled out in its 2000 report, “Principles and Standards for School Mathematics.”

“Is it a shift in thinking for them? Not necessarily,” said Matt Christiansen, math coordinator for Greeley-Evans School District 6. “It just clarifies some things.”

The Focal Points study points out inconsistencies in curriculums across the nation. It notes wide-ranging differences in how math topics are defined and what students are expected to learn.

The council’s study looked at curriculum standards in 10 states, not including Colorado, and found the number of math learning expectations for fourth grade ranged from 26 to 89.

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Focal Points for pre-K-8 narrows down what teachers should emphasize to three basic skills for each grade level.

“NCTM has made clear that (Focal Points) is a document that can be used to guide curriculum to help states as they develop standards and develop commonality,” Christiansen said.

The “fuzzy math” tag came in response to a late-1980s National Council of Teachers of Mathematics report that advocated “reform” math. The reforms shifted from skill-and-drill basics to an open-ended system where students delved into an assortment of math topics and real-life problems.

Reports in recent years about trends in international math gave critics more artillery. The reports highlighted the performance gap between U.S. students and their global counterparts. The United States ranks 15th in eighth-grade math skills, while Singapore ranks No. 1 and South Korea is No. 2.

Wes Tuttle, principal at Meeker Elementary School in Greeley, is a former math teacher and former District 6 math coordinator. He said schools in Asia take a few math concepts and study them from all angles.

“They’re getting a very deep, rich understanding of a particular concept,” Tuttle said. “So the advantage there is the kids have a much deeper understanding of that skill.

“That’s a definite advantage here of the Focal Points… We’re zeroing in on three things you need in third grade or fifth grade.”

For example, the Focal Points document says, fourth-grade students should be able to:

* develop quick recall of multiplication facts and related division facts, and have fluency with whole number multiplication;

* develop an understanding of decimal, including the connections between fractions and decimals;

* develop an understanding of area and determine the areas of two-dimensional shapes.

The curriculum focal points in fourth grade build on those skills.

District 6 is shifting to the “Investigations in Number, Data and Space” program in elementary schools and uses “Connected Math” in middle schools. They are standards-based programs, meaning they are tailored to state assessment standards.

“They are more along the lines of taking a couple standards and going deeper with them,” Tuttle said of Investigations and Connected Math. “They’re not zeroed to just three (skills) — they’re broader than that — but they are more along the lines of what NCTM envisioned.”

Investigations, developed by a Crambridge, Mass., nonprofit, “helps kids get a conceptual understanding, not just ‘Here’s a procedure, now practice it 15 times,’ ” Tuttle said.

Christiansen said it’s important to address “why” multiplication tables are relevant to students. Standards-based programs probe into the why, he said, and are supplemented with basic-fact instruction.

“That’s been a criticism of many standards-based programs — that they ignore basic skills,” Christiansen said. “That has not been the case. It’s never been NCTM’s position that we ignore basic facts.”

Jeff Farmer, director of the University of Northern Colorado’s school of mathematics, said the National Council of Teachers of Mathematics report continues the trend toward better math instruction at the primary and secondary levels.

It’s essential that educators not be tempted to use the standards as a list of topics, he said, because that misses the point of reform. Farmer noted that the council’s report is wisely written from the perspective of what students need to learn.

“Hopefully they’ve put out a pretty good example of how you can focus things and say these are the focal points,” he said. “If districts say we’re going to take those focal points as a drill … you lose all those things that standards have worked so hard to put in.”